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In terms of snow - April 14th is the last week of the season. It will be warm and the snow will be melting quickly. However, if you are interested mainly in green runs and lessons, this may be a good time to bring the little ones out to introduce them to skiing.

Park City Mountain Resort makes a ton of snow during the season. They "store" it up the mountain and push it down to the base as the season ends. I'm fairly confident there will be snow to ski at the end of Feb. - just not a lot of it.

You'll definitely have snow but you're also pushing it on late season. Plan on it being soft and challenging - not the greatest time to visit if you're just introducing the kids to the sport. All three resorts plan to be open that week, but it's a week later than usual for all of them. Plan on it being especially sketchy on the bottom half of the mountain.

Canyons is an interesting option as it does ski school at mid mountain at the top of the gondola, where conditions will be better than at the base. In general, all three resorts have comparable ski schools and comparable green terrain.

As mentioned, you are pushing the closing dates for the Park City resorts. It's not that they won't have the snow, they just don't have the business to justify keeping a full staff for a quality operation. If it's a huge snow year, they might push back the closing date by a week or so. Their bases are at least 1,000 feet lower than many of the other resorts around, which means the snow quality goes quicker. The one area that will be open is Snowbird. They often continue operations until Memorial Day weekend. You could ski the remainder of the season in PC and then drive the hour to Snowbird. Brighton might be another option, and will have far more suitable green terrain for a beginner and is considerably less expensive than Snowbird.

You read my mind I was just thinking about whether a mid-April trip was feasible. For those of you who are wondering "why so late" it is due to a unusual calendar quirk that places spring break very late this year due to Easter. Not very helpful for those of us who want to take the kids skiing!

The scheduling issue is further compounded by the lack of snow in California - unless things change the resorts will be closing early in Lake Tahoe in 2014. So that only leaves Utah and Colorado as potential options - assuming you continue to get snow.

I like Park City due to the ski-out option but the advice about Snowbird (and Alta) is quite sound - more likely to have good late season conditions. Perhaps just play it by ear as the lodge is unlikely to sell out early for those dates.